But the Angels continue to sound like a club that isn't counting on re-signing the vaunted right-hander.

Obviously, things can change very quickly, and Angels general manager Jerry Dipoto has a recent track record of being very coy about his pursuit of big-name free agents (see: Albert Pujols, December 2011). But the price tags continue to be sky high -- the latest being Haren's $13 million contract and Shane Victorino's reported three-year, $39 million deal with the Red Sox -- and the Angels appear content with simply adding one middle-tier starter and one back-end reliever.

On Tuesday afternoon, Day 2 of the Winter Meetings from the Gaylord Opryland Hotel, FOXSports.com's Jon Morosi tweeted that the Dodgers "have become [the] clear favorite to land Greinke," echoing a sentiment that has been widely reported and speculated upon for most of the offseason. Jon Heyman of CBSSports.com later wrote that the Greinke sweepstakes appears to be a two-horse race between the Rangers and Dodgers.

The Angels, who continue to be portrayed as a dark horse, want to avoid what happened last season, when they committed a lot of money to the rotation and were essentially tapped out in August, unable to add to a bullpen that badly needed an upgrade. If Greinke's price gets to $150 million, they're likely out. If he's willing to settle for something less, they still have a chance.

"We're not going to get hung up on one target as a stand-alone," Dipoto said. "We're going to keep our mind open and we're going to make good decisions as to how we get that 12-man [pitching] depth."

Sitting in his suite during his daily briefing with reporters, Dipoto didn't go into much detail, only reiterating the fact that he's looking for one more starter and one more reliever.

He also didn't sound like he was particularly close on anything.

"We'll get the right pieces," Dipoto said. "It's just a matter of when."

Anibal Sanchez and Kyle Lohse remain options for the Angels, but their price tags may get bloated if Greinke signs for the record money he's been linked to. That would seemingly make the likes of Ryan Dempster, Edwin Jackson, Brandon McCarthy, Shaun Marcum and Joe Saunders more suitable options.

For the bullpen, Mike Adams, Sean Burnett and Koji Uehara remain in play. But what Dipoto spends on his final rotation spot will affect what he can spend on a reliever.

"We're trying to find the right combination of players that fit our needs," Dipoto said. "Some of that is going to be a situation of timing. Which comes first, is it the starter, is it the bullpen? We haven't even ultimately defined whether we're going to make two moves. There's the possibility that we can do more than two. It's very unlikely that we do more than three, but the combination of events are kind of limitless, really. So it's impossible to speculate on what you might do, and a lot of it is going to depend on which is the first domino to fall."

The big domino is Greinke, but Haren opted against waiting and instead chose to slide in the middle of a vaunted Nats rotation.

Haren was one of baseball's most consistent starting pitchers from 2005-11, posting a 3.49 ERA while averaging 14 wins and 226 innings per season. But he struggled from the onset in 2012, due partly to a bad back and another slight dip in velocity, finishing 12-13 with a 4.33 ERA in 30 starts despite turning it around down the stretch.

Before declining his option for next season, and before a proposed trade to the Cubs for Carlos Marmol fell through, the Angels offered Haren a one-year, $4 million deal with an $8 million vesting option, a source said. Dipoto confirmed on Tuesday that the Angels circled back with Haren throughout the offseason, meeting with him as recently as Tuesday, and a source said they slightly improved on their original offer.

But Haren moved on -- and the Angels are still trying to find a fit.

"We hadn't closed that door, nor did Danny," Dipoto said. "I wish him well; he did a great job during his time here. But we're singularly focused on making the Angels better. How the market allows that to happen is going to up to the market, but we're focused on the targets that we are focused on."